SSE JE Electrical Engineering 10 Dec 2020 Papers

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Question : 190 of 200

Marks: +1, -0

Determine the resistance R in the given circuit, if the voltage at node-b is

\V_\b = 5 \V.

8 Ω
2 Ω
5 Ω
4 Ω

Solution:

The given question is

\I_1 = 4 \A

\I_4 = 4 \A

\V_\b = 5 \V

\R_1 = 5 \Ω

\R_2 = 10 \Ω

KCL at node ‘a’

\I _{1}+ \I _{2}+ \I _{3}=0

4+{ \V _{ \a }}/{ \R _{2}}+{ \V _{ \a }- \V _{ \b }}/{ \R _{1}}=0

4+{ \V _{ \a }}/{10}+{ \V _{ \a }-5}/{5}=0

40+ \V _{ \a }+2 \V _{ \a }-10=0

3 \V _{ \a }+30=0

\V _{ \a }=-10 \V

KCL at node ‘b’

\I _{3}+ \I _{4}= \I _{5}

{ \V _{ \a }- \V _{ \b }}/{ \R _{1}}+4={ \V _{ \b }}/{ \R }

{-10-5}/{5}+4={5}/{ \R }

{-15}/{5}+4={5}/{ \R }

1={5}/{ \R }

\R = 5 \Ω

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